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1

Road to chaos in a Duflng oscillator with time delay loop

Borkowski Łukasz

Mechanics and Mechanical Engineering

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2021

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Vol. 25, nr 1

84--87

EN

This article examines a single Duffing oscillator with a time delay loop. The research aims to check the impact of the time delay value on the nature of the solution, in particular the scenario of transition to a chaotic solution. Dynamic tools such as bifurcation diagrams, phase portraits, Poincaré maps, and FFT analysis will be used to evaluate the obtained results.

2

Determination of Hopf bifurcation sets of a chemicalreactors by two-parameter continuation method

Berezowski Marek

Chemical and Process Engineering

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2020

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Vol. 41, nr 3

221-–227

EN

A two-parameter continuation method was developed and shown in the form of an example, allowingdetermination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations weremade for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the rangeof oscillation in the reactor was determined. The results were confirmed on the bifurcation diagramof steady states and on time charts. The method is universal and can be used for various models ofchemical reactors.

3

A Novel Chaotic System and its Modified Compound Synchronization

Sun Junwei, Li Nan, Wang Yanfeng, Wang Wei

Fundamenta Informaticae

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2019

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Vol. 164, nr 2-3

259--275

EN

In this paper, a new chaotic system is proposed, whose dynamical behaviors are discussed with the change of the parameters in detail. The specific effects of different parameters on the system are also discussed. By adjusting these parameters of the proposed circuit, this nonlinear circuit can produce the different dynamical behaviors, such as, hyper chaotic behavior, periodic behavior, transient behavior, etc. Furthermore, a novel kind of modified compound synchronization has been investigated, where the multiple chaotic systems have been considered for different combination modes: the compound system of four scaling drive systems and one response system. The corresponding controllers are designed to realize the modified compound synchronization. The theoretical proofs and numerical simulations are given to demonstrate the validity and applicability of the proposed chaotic system and the modified compound synchronization.

4

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

Tacha O. I., Volos C. K., Stouboulos I. N., Kyprianidis I. M.

Archives of Control Sciences

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2016

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Vol. 26, no. 1

95--115

EN

In this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called ‘dissaving’ is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system’s behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.

5

Dynamice of three unidirectionally coupled Duffing oscillators

Borkowski Ł.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 2

125-132

EN

This article presents a system of three unidirectionally coupled Duffing oscillators. On the basic of numerical study we show the mechanism of translation from steady state to chaotic and hyperchaotic behavior. Additionally, the impact of parameter changes on the behavior of the system will be presented. Confirmation of our results are bifurcation diagrams, timelines, phase portraits, Poincare maps and largest Lyapunov exponent diagrams.

6

Bifurcation diagram for drive system

Houfek L., Kratochvil C., Krejsa J., Navrat T

Modelling and Optimization of Physical Systems

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2008

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z. 7

43--46

EN

The paper is focused on analysis of dynamic properties of drive systems. It describes the possible ways of stability analysis and possible ways of analysis of bifurcation of steady states and possible occurrence of chaotic behavior.

7

Vibrations Induced During a Stability Loss of Periodic Trajectories of the Manipulator

Szumiński P., Kapitaniak T.

Machine Dynamics Problems

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2004

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Vol. 28, No. 2

65-85

EN

We present how to avoid dangerous situations that occur during a robot periodic motion and are caused by different kinds of vibrations. Theoretical analysis of stability regions of nonlinear and linearized system and of the ways of inducing vibrations during a stability loss of periodic trajectories is developed. For practical control of motion a common part of areas of stability received for nonlinear and using linearized Poincare map can be taking into considerations. The areas of stability are identificated by the bifurcation diagrams and Poincare maps. Stability regions of periodic trajectories as a function of varying parameters of the system are investigated . As a practical tool for the control of stability, a spectrum of Lyapunov exponents is proposed. To illustrate our method theoretically and numerically, a model of the RRP-type manipulator has been considered.